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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">V'</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>, <font color="Maroon">W'</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">V'</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#G2">RLSStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V</font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">V</font> #)
 ;<br/>

<b>let </b><font color="Maroon">W</font> be    <a href="rlsub_1.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/>

<b>assume </b><a NAME="E2:39"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">W'</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#G2">RLSStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">W</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">W</font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">W</font> #)
 ;<br/>

<b>hence </b><a NAME="E3:39"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W'</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">V'</font>
 <b>by </b><i>, <a class="ref" href="rlsub_1.html#D2">RLSUB_1:def 2</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="rlsub_1.html#D2">RLSUB_1:def 2</a><br/>

<b>thus </b><a NAME="E4:39"/>
the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">W'</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">V'</font>
 <b>by </b><i>, , <a class="ref" href="rlsub_1.html#D2">RLSUB_1:def 2</a></i>;<br/>

<b>thus </b><a NAME="E5:39"/>
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">W'</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">V'</font> <a href="realset1.html#K1">||</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W'</font>
 <b>by </b><i>, , <a class="ref" href="rlsub_1.html#D2">RLSUB_1:def 2</a></i>;<br/>

<b>thus </b><a NAME="E6:39"/>
the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">W'</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">V'</font> <a href="partfun1.html#K2">|</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><a href="supinf_1.html#K3">REAL</a> ,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W'</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i>, , <a class="ref" href="rlsub_1.html#D2">RLSUB_1:def 2</a></i>;<br/>


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